Methods of the mentioned type are known among others from the German magazine "Werkstatt und Betrieb", 118th year (1985), Number 8, Pages 505-509, in particular Page 506, and from DE-37 34 653 Cl, which corresponds to U.S. application Ser. No. 07/247 875, filed Sept. 22, 1988. In spite of a guided radial infeed of the tool, problems occur again and again in practice due to burrs remaining in the tooth gaps of the workpieces, which burrs cause a partial destruction of the tools coated in most cases with CBN. The mentioned problems occur in particular in workpieces which are hardened after milling; in those workpieces which were also prefinished before hardening, remaining burrs are rarely found, since they are "cut off" or pressed away during finishing. Because precision working is to be performed with an abrasive tool after the hardening, a prefinishing, however, as a rule does not take place for cost-saving reasons, especially since during transport and during handling on the way to and in the hardening shop, damage, mostly in the form of dents or the like and the resulting outward bulging of displaced material adjacent the dent, as shown at B in FIG. 4, in particular on the tooth edges, cannot be avoided 100%.